This invention relates generally to signal sampling techniques, and more particularly the invention relates to variable density signal sampling. The invention is applicable to the sampling of any signal but has particular applicability to magnetic resonance imaging (MRI) signals. The invention will be described in context of MRI signals and applications, but is not limited thereto.
Assuming that a signal is band-limited, uniform sampling at the Nyquist rate is typically employed. However, to reduce the sampling rate below the Nyquist rate, prior knowledge of the signal is advantageous in establishing optimal sampling locations.
In MRI, a continuous signal is sampled at arbitrary locations chosen by design. However, each sample in MRI is very costly since only one sample can be acquired at a time. To obtain a higher resolution, or a bigger field-of-view image, more samples need to be collected, but longer scan time results in problems such as motion and flow artifacts. Furthermore, in cases where the physiological parameter of interest has a shorter time constant compared to the scan time required for the given resolution and field-of-view, it is necessary to reduce the number of sampling points beyond the limit imposed by the Nyquist sampling rate.
To reduce the number of sample points, many different techniques utilizing prior knowledge of the signal have been proposed and used. These techniques are mainly based on the observation that the low spatial frequency components have bigger energy. Therefore, these techniques mostly try sampling more densely in the low spatial frequency region while under-sampling in the high spatial frequency region. These techniques are generally known to work well. Yet the problem of determining the optimal sampling pattern has not been solved heretofore.